Question

Two similar spheres having +Q and -Q charges are kept at a certain distance. F force acts between the two. If at the middle of two spheres, another similar sphere having +Q charge is kept, then it experiences a force in magnitude and direction as ______.

Options

• zero having no direction.

• 8F towards +Q charge.

• 8F towards -Q charge.

• 4F towards +Q charge.

Answer 1

Two similar spheres having +Q and -Q charges are kept at a certain distance. F force acts between the two. If at the middle of two spheres, another similar sphere having +Q charge is kept, then it experiences a force in magnitude and direction as 8F towards -Q charge.

Explanation:

Initially, force between A and C,

F = `"kQ"^2/"r"^2`

When an identical sphere B with a charge of +Q is placed in the middle of the line connecting A and C, the net force on B is

`"F"_"net" = "F"_"A" + "F"_"C" = "kQ"^2/("r"/2)^2 + "kQ"^2/("r"/2)^2 = (8"kQ"^2)/"r"^2`

= 8F

The direction is shown in figure.